What is the rate at which energy is dissipated in R2? What is the rate at which

Question

What is the rate at which energy is dissipated in R2?

What is the rate at which energy is dissipated in R3?

What power is emitted by battery 1?

What power is emitted by battery 2?

(Image included with problem) In the circuit in the figure, V1 is 31.20 V, V2 is 29.30 V, R1 is 24.0 ?, R2 is 72.0 ?, and R3 is 41.0 ?. Both batteries are ideal. What is the rate at which energy is dissipated in R1? What is the rate at which energy is dissipated in R2? What is the rate at which energy is dissipated in R3? What power is emitted by battery 1? What power is emitted by battery 2?

Explanation / Answer

For the junction...

i1 = i2 + i3

i1 is top left moving right, i2 is middle moving down, and i3 is top right moving right by my designation

Left loop counterclockwise

-31.2 + 72i2 + 24i1 = 0

Sub in for i1

-31.2 + 72i2 + 24i2 + 24i3 = 0

-31.2 + 96i2 + 24i3 = 0

Solve for i2

96i2 = 31.2 - 24i3

i2 = .325 - .24i3

Right loop counterclockwise

29.3 + 41i3 - 72i2 = 0

Sub in for i2

29.3 + 41i3 - 72(.325 - .24i3) = 0

29.3 + 41i3 - 23.4 + 17.28i3 = 0

58.28i3 = -5.9

i3 = -.1012 Amps

Then i2 = .325 - .24(-.1012)

i2 = .349 Amps

Then i1 = .349 - .1012 = .248 Amps

So for the power in R2 = I2R

P = (.349)2(72) = 8.77 Watts

The Power for R3

P = (.1012)2(41) = .420 Watts

The Power in V1 = IV

P = (.248)(31.2) = 7.74 Watts

Power in V2

P = .1012(29.3)

P = 2.97 Watts

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